10:00 - 12:00 Short CourseModel Theory, p-adic Integration, and Applications to Algebra and Number Theory School

MATHEMATICS

This course is concerned with model-theoretic results for local fields and finite fields, and p-adic and motivic integration. The main results concern analytic properties of Euler products and applications to various zeta functions and Dirichlet series in algebra and number theory.
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Astrophysical jets emerge from magnetized accretion disk systems. It is now commonly accepted that magneto-hydrodynamic (MHD) processes are essential for the launching, acceleration and collimation of the outflows and jets from accretion disks. I present the results of fully 3D magnetohydrodynamic jet launching simulations of a jet source orbiting in a binary system. The simulations consider a time-dependent gravitational potential of the binary, thus all tidal forces of the orbital motion that are experienced in the non-inertial frame in the jet-launching primary. The simulations run over a substantial fraction of the binary orbital period. ...

In this talk, I will give a review of my recent joint works with Wentao Fan and Matilde Marcolli on a rationality phenomena and appearance of periods and motives in the heat kernel expansion of the Dirac-Laplacian of Bianchi IX gravity models with SU(2) symmetries. In the case of Bianchi IX gravitational instantons, which, in a succession of works by physicists and mathematicians, are characterized in terms of theta functions with characteristics, the terms in the expansion give rise to modular forms of weight 2, which we write explicitly in terms of Eisenstein series and the modular discriminant. ...

The Large Hadron Collider at CERN carries out nucleus-nucleus collisions and proton-nucleus collisions at unprecedented energies. I review some of the key observations in these experiments, and I explain why they are interesting from a theoretical point of view. I discuss in more detail the anisotropies in particle distributions: these anisotropies originate from quantum fluctuations in the projectiles, followed by expansion into the vacuum, much in the same way as the anisotropies of the cosmic microwave background of the Universe, thus drawing an interesting parallel between high-energy physics and cosmology.